PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of they rolls result in snake eyes? Calculate an appropriate probability to support your answer. ALTERNATE EXAMPLE (page 411) Aussie instant lottery Calculating binomial probabilities PROBLEM: The Australian Official Lottery has scratch-off instant lottery tickets that can be purchased for $1. The probability of winning a prize is 1 in 4. (a) Mr. Urban is feeling lucky one day and decides to purchase 100 of the scratch-off instant lottery tickets. Find the probability that fewer than 20 tickets are winners. (b) In fact, Mr. Urban won a prize for only 19 of the tickets. Does this result give convincing evidence that the probability of winning is less than 1 in 4? PROBLEM: Mrs. Patenaude asked each of the 28 students in her AP Statistics class to toss a coin and record the result. Assume that all the coins are fair. Let X = the number of coins that landed heads. Here is a histogram of the probability distribution of X: (a) Calculate and interpret the mean of X. (b) Calculate and interpret the standard deviation of X